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The torsion tube can apply to the torso but also to the limbs and to the limbs and torso considered in a continuum.

The double pendulum can be considered as the legs from hips to ground plus the torso from hips to head. Each limb may also be separately a double pendulum, or all of them together form a chain of dependent pendula.

At first glance, these models would seem very different, a torsion tube quite static, the double pendulum quite dynamic, but the structure and dynamic of these models are, in fact, closely related.

This is a stress diagram of a torsion tube:
The the effect of the torque creates shear on the radial and longitudinal axis of the tube. The diagonal figure shows the resulting linear stresses of the shear -- tension in one diagonal and compression on the other. If you extend these diagonal lines around the surface of the tube, (and torsional shear is always greatest at the surface) then you get two interlaced spirals around the body of the tube.

One spiral is in compression and the other spiral is in tension. The two lines of stress are oriented 90 degrees from one another, and they are both 45 degrees off the longitudinal axis of the tube.

"Wait!" you say, "What about the double pendulum?" Well, since you asked…

Two linked pendula that swing with a 90 degree offset from one another make a dynamic curve, called a harmonic curve, also called a Lissajous figure. It can take on very many shapes, all mathematically similar, but one form of the harmonic curve looks like this :

Two components of opposed stress at 90 degrees form an interlaced spiral relationship, so do linked pendula operating at 90 degrees offset.

Double pendulum action occurs in, dare I say, all actions of the human body's balance and limbs. Torsional stress occurs in all actions of the human torso and limbs. This understanding shows that the lines of interlaced compressive and tensile stress (in-yo) link the two sides of the body without muscular contribution -- if the form of the body is collinear with the stresses.

To illustrate, place both arms in tegatatana, turn palms and elbows out, raise one arm and lower the other -- Voila! An upper spiral engaegd at the "upper cross" of the back. Now in this position, stand with feet at shoulder width, and turn on the heels and balls of your feet without stepping, twisting down until your kneecap touches the back of the other knee. You are a stable continous spiral form coincident with the torsional stress lines. This is tenchi posture - and what has been shown somewhat statically with very large form, can also be managed dynamically (with greater developed control) in much smaller progressive spiral forms or waves.

If one addresses a line of stress, say compressive stress, and pushes on it (compressing), well, you just pushed against what is already "sprung" to push back. If, on the other hand, you compress the tension line of stress, you relieve the stress on the structure, and it cannot resist without reversing its internal stress. Conversely, if you exert tension along the tension line -- it is already "sprung" to pull back. If you tense the compressive line however, you relieve its stress, which it is impossible to resist, unless the internal stress is reversed.

If I actuate the structure using this same mode, by prestressing the structure and connection along a compression line of stress, by relaxing the compressive stress -- the structure extends ("pushes") along the compression line, Conversely, if I prestress the structure in tension, and engage along the tencison stress line, and relax, the structure contracts ("pulls") along the tension stress line. In fact If I keep the intergity of the body whole, I do both at the same time on different sides.

This mode is distinct from using musculature to "push" or "pull" because the pre-stressing of the structure allows it to "relax" into the load along an appropriate line of stress, such that it cannot over-actuate, as muscles do if making active compensatory (resistant) strains.

If the structure is linked (jointed), and an applied extension or contraction is applied so as to relieve the target's internal stress along the torsional lines --the reduction of stress causes the limb (or torso) to tend to buckle (gyrate) outside the spiral torsional line of stress supporting it against the loads-- at which point it can exert neither tension nor compression in response, (and the sudden discontinuity typically reverses the applied stress profile, often catastrophically).

Reversing stress in a continuous mode without buckling, requires a smooth transition of form and energy at the same time. It is the form of a wave, spiral, like the stress lines, but cycling from positive to negative (like the top or bottom of the Lissajous curve noted above, or the top and bottom limits of the torsion tube structure, since all the stresses have to be resolved within the structural limits. If it does not resolve, then the structure must move to relieve the structural stress. Thus, at the major discontinuities -- the lower limit of the structure, (Earth) and the upper limit of thew struture ( heaven) compression on one side spiral resolves to tension on the opposite side spiral at the top of the structure, and tension on one side resolves to compression on the other side at the bottom.

At any discontinuity in the linked structure, the same reversal can occur (and already exists -- at a small amplitude). A small cycle of stress waves (kokyu in-yo ho) will "find" a discontinuity. A resonant cycle of stress waves will maximize the discontinuity signal (furitama). A counter-phase pulse of stress waves (or conversely the intersection of a counter-phase shape, which is equivalent) into the discontinuity will cause it to buckle and lose all structural integrity allowing displacement by the connection struture. (kokyu tanden ho)

Because the body's tendon stretch reflexes are conditioned to respond to sudden losses of structural integrity, they come into play. If a tendon is stretched suddenly there is a reflex action (e.g. -- the knee reflex), too fast for the conscious compensation to stop. A sudden wave of stress through the structure of sufficient amplitude AND at the resonance frequency (the structure itself amplifies the wave) induces a non-linear tendon stretch, triggering the stretch reflex associated with any tendon which is already in discontinuity.

Because the triggering phase is followed by the reversed phase of the stress wave, if the reflex is triggered, the reflex overactuates with respect to the oncoming counter-phase of the wave. The joint buckles out of the line of stress, and structural integrity is lost. The mechanism of structural integrity is exploited in a critical way to destroy that integrity.

This is one way to look at the integration of structure and dynamic in Aiki. The discussion on strikes and resonance in my blog looks at other issues, as does a discussion there on mass transfer and angular momentum chains. One pointt that I dealt with off-line with another poster here, helpfully pointed out an error in my interpretation of the mass transfer math, (adding an additional square term which was a already implicit in the interaction). The intuitive appeal of the error, I now realize, was my sense of the size off the disparity in input to reaction in actual engagements. That disparity, i now realize has much to do with the resonance and reflexive effects on the target , more so than the actual effective energy of the delivered input.

All of these points are suitable for adaptng a structure to structural stress or dynamic loads as they are in disrupting it with structural stress or dynamic loads. The interplay can become quite complex between individuals with good training.

The torsion tube can apply to the torso but also to the limbs and to the limbs and torso considered in a continuum.

I have to say the above descriptions do seem to match up pretty well, especially the torsion tube, which is consistent with Dan's description of fascial bands spiralling up the body.

I myself have lately been thinking of the dynamic as being like a basket of woven bamboo (more or less a torsion tube) with lots of flex, but also a lot of self-interference which acts to support the structure. Any stress you place on the bamboo basket distorts the basket only so far. Of course, the basket has no ability to "spring back" into the input force, but it's only a model.

Overall, I would say that the torsion tube model is consistent but I think you go a little too far with concerns for resonance and (elsehwere) gyroscopics.

If I read this right, it sounds like you just need to get some hands-on with recognized experts (Dan) in this field and see how well your theory can really be expressed in the body.

David

"That which has no substance can enter where there is no room."
Lao Tzu

That would be the effects of angular momentum from reading too much Erick Mead. To quote the good counselor (with affection, sir, not disdain):

[i][A fine balance must be struck and always try to keep them teetering at the edge of the sensation they are feeling for. If you don't do that and keep the dynamic toward ever less "firm" (apart from atemi) then the dynamic naturally tends toward the other gradient -- the testerone-competitive monster tends to jump in and starts the "me-bad" dynamic. It is not as helpful to development of good musubi connection.

Quote:
Can you define "juji" and its application?

Several of O-Sensei's Doka mention it, one even calls the art "jūjido." Juuji or jūji ( 十字 ) is the cross-shape or sign of the cross (for those so inclined). It is a symbol, a physical principle, a template for technique and spiritual basis for contemplation of practice.

As kanji, 十 juu not only means "cross" and "ten" but also "whole" or "complete." As a symbolic image in Japan, the horizontal symbolizes Earth, and the vertical symbolizes Heaven, i.e. -- tenchi, the union of heaven and earth at the center. It is another means of depicting in-yo with the dynamic elements of the opposed eight powers (bagua) built in.

As a physical principle, juji depicts the action of perpendicular component forces. In motion in a linear plane, perpendicular forces resolve to linear diagonal forces in proportion to magnitude of the two components. Judo in contrast focuses on using or creating an offsetting pair of opposed forces (a couple) to initiate rotation. In an already rotational or vibrational frame, force perpendicular to the rotational or vibrational plane have resulting perpendicular forces that are not linear, because of the inherent angular momentum, the resultant force depends on where along the radius of rotation/vibration the output is taken. The fact of that momentum also allows the sytem to absorb a great deal of energy withou out readily perceptible change.

Juji in aikido presupposes that there is an existing rotational or vibrational energy to receive and gyroscopically transform a single input force into perpendicular output at a variable scale of radial amplification. That vibration or energy is ki no kokyu, or if you prefer the technical description, the physical application of the principle of virtual work on an instantaneously and infintesimally rotating body (at each joint rotational articualtion in turn and ultlimately at the collective rotational center of mass (tanden).

As a template for technique, heaven and earth are joined statically by their intersection at the center, and thus the center is arrived at by moving directly along the line. The conduit for kokyu tanden is established by feeling of that angle "lock" where the components of force are all cancelled in one dimension, leaving a complete freedom of movement there. The vertical dimension and the horizontal dimension of the figure are also joined dynamically by the fact that one becomes the other by simple rotation. Thus, the center is arrived at by spiral motion. /I]

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IMO, gyroscopics comes up because of how he describes the force transformation in the body.
I think the idea is interesting; 'controlling orthogonal force combination'.

...Except with juuji as defined we are not providing the other vector b but rather providing the inverse of what was usually the resultant rotation/torque (i.e. via a dantien based manipulation); which results in an output vector, d, which is weird and unexpectedly will throw uke.

where the inverse curl is provided by a dantien rotation and bodyskill. Yep. I know. it's only the vaguest of impressions of an actual specific thought... and no; i am not selling this this as useful or correct...just some thoughts i had. (of dubious value)
[/spoiler]
Anyhoo...what actually sparked all that conjecture was a comment by Gernot (which i probably misunderstood!)

In the end it is about carrying and generating load through shape, static at first, then dynamic -- and not by material strength or levered actuation limits. The loaded shape that achieves zero internal shear (the funicular curve, or no bending moments, as you prefer) beats a shape with any shear at all.)

But conversely, the shape with a fully balanced shear load actuates in "unshearing" ("relaxing" if you will) and most effectively in untorquing, especially if you relieve the imposed load stress on the complementary torsional shear stress spiral -- which is, frankly, fairly spooky for most people to feel, since I relax/compress where they are pushing, and relax/stretch into them where they were not. It doesn't fit their linear image of actuation and they get wide-eyed as their balance creeps away from them. Clarke's law applies.

Shape-wise there are three fundamental cases of shape (or image) for using shear modes actively, passively or "neutrally." Any of the three cases can be applied in any of the three modes. The slack case (chains & whips), the solid-state or "charged" case (the torsion tube) and lastly a middle case, which is neither slack nor "charged" but proportionately and inversely converts two dimensional displacement from plane to orthogonal plane (asagao). They all are founded in 90 degree relationship terms -- and in the context of complex harmonics and resonance that relaitonship is both temporal and spatial.

Discussion of "ground" I read as the "solid state" or "charged" case (Shioda's favorite mode), and "gravity" as the slack case.

Shear is also transmitted by cyclic action or pulse -- atemi, furitama, which exhibit definite resonance uses, and several other means, which do not, such as funetori, ude furi, saya undo, etc. Once you begin to talk about dynamic shape then the chain-ish multi-pendulum rotational momentum transfer concerns come in. Gyroscopic moment(um) conversion arises in interactions that are explicitly rotational or potentially so (poised moments).

The asagao (morning glory) manner of action (seen in sanchin also) It is illustrated by the continuous form from fully extended twisting punch to fully withdrawn splayed hands. As far as I am aware this has NO good analogue image in foundational Western physical models -- outside of modern deployable structure or tent design -- but it deserves a place, because IMO it is more basic than it seems at first glance. Closest that any image or model comes visually is wingtip vortices -- also a shear phenomenon.

Discussions of "intent" I read as adaptive loading. I see far more adaptively reflexive about good work (takemusu) than in the ordinary meaning of "intent" as voluntary action (which I find very unhelpful in that sense, and have the distinct impression that it is a training modality or model for the others that is superseded by more reflexive adaptive action ).

Discussions about the action of "fascia" I read as the feel of "set" (or "loosening," conversely) in the "correct" shape for the imposed (or generated) load. Shear is always highest at a boundary of action -- so the sensory impression imputed to the "fascia" would be quite correct, mechanically. Speculation as to other biological action of actual fascia tissue cannot be ruled out, though still poorly understood. To some extent it can be seen as reaction of the soft structures in a driven resonance (like vibratory tool hand-clamping (which is not merely mechanical but neuro-muscular/fascial and is trained with furitama), tekubi furi, etc.

And if dynamic access to shift shear loading (even very slightly, and cyclically) is unconstrained to the whole of the body as a mechanism, (through resonance) then the shear-vulnerable linkage(s) will reveal and the whole load can be fed progressively through that hole in the structural dam. Conversely, counter-damping can prevent that access.-- I read Dan's ability to be very powerful in this mode -- what little he speaks of it terms that are not coded in his own vocabulary -- not a criticism -- he is actually intelligible me -- if lacking rigor,which is why I am apparently not intelligible to him. When he speaks of resisting a push, in part, I read counter-damping as much or more than load adaptation. If I resist the static push methodology, as such, it is because of weapons avoidance concerns that are a deep part of our dojo's specific history, and that mode is counterproductive to instinctively not being where a weapon would go.

Training-wise I emphasize static shape loading and simple shifting initially, which is much easier to perceive for most people (and fairly common in most places I have trained, actually). Kokyu undo/ aikitaiso are followed and corrected through every waza exercise, and most of the "waza" we perform begin in some distinct variation from "canonical" form. No rote movements.

In what I am doing, I have taken fairly new folks with no prior training and within about three to five months with the structural emphasis have them comfortable with koshinage on guys that outmass them by seventy or eighty pounds. Comfortable, not indestructible.

Less commonly, I emphasize loading and unloading on the opposed torsion compression/tension spirals in connection. I work on "charging" and relaxing or collapsing the structure actively ( and in complement to the opponents mode, be it "charged" or slack) -- acting in furitama rhythm to create compressive or tensile resonance at contact -- which tends to induce buckling for a kuzushi -- anywhere there is a structural vulnerability -- by all accounts I expect Dan doesn't have many of those.

Ikeda has often illustrated when he visited, his "falling leaf" pulse action, which is of this variety, and began my thoughts on resonance and its importance about seven years ago. everything was built up from there. These two new girls I mentioned above have gotten the essentials of driving the reflexive flexors (slight aiki sage) with a resonant weighted shudder into the shoulder. They aren't dropping people like decapitated buffalo, but they are gaining definitive kuzushi with a projected and weighted touch, and with very little prior background. We are working them up to better "charged" and "slack" aiki age -- particularly in kokyu tanden ho and tenchi nage.

The main difference I see in what the "group" is doing (I don't pretend to belong) is that I have a structural ideal that is inherently adaptive (if perceived) and -- broadly speaking -- I am hearing the other school of thought talking about an adaptive ideal (if perceived) that inherently structures. Maybe too broad but that is some of the real disconnect -- it lies in our complementary presumptions, I think. Wherefore we seem ass-backwards to each other -- because we are, basically The other approach has a long head start, practically speaking -- I'll be the first to acknowledge -- but this approach speaks to things and learning styles the other one does not -- and also has the advantage of not having been tried, so ...

I feel like I need a Physics degree to understand what's going on in here... But I like it. In a way I can catch glimpses of how we can describe what has been largely an indescribable element of Aikido.

What I would have generally described as the non-mechanical aspect of Aikido i.e. the Aiki or Mind-Energy-Body unity part is now hereto being described aptly as being mechanical/physics still. Does this help in the learning of it? Apparently so if Erick's students are to be believed.

Does it require actual/extensive physical instruction or can it be done just by understanding the concept as introduced by Erick to learn though... I wonder.

A large part of learning aiki is to take ukemi from the sensei. To feel how its done, to hear his explanation on how its done, and then to emulate, fail, experiment, get feedback and ultimately achieve some semblance of success.

I confess, I really can't understand everything that's been described above even though I suspect is been largely watered down for the benefit of us laymen. But what has been said is largely reinforcing my growing realisation that 'ki' has a very large number of subsets. A major part for the beginner-intermediate subset is how we train the physical body to react under force/pressure and how we use our own force efficiently.

Grounding incoming force and projecting the 'earth' into various parts of the body, extending it beyond our body into uke, taking uke's center, leading not forcing, wave/bouncing, impulse/ateru... I've seen it, felt it, heard it described from the esoteric to the scientific way, and it boils down to how well we can duplicate what we feel. If we can't make our body do what we are thinking of doing, the scientific explanation written like a manual might as well have been written in French.

I like training with bigger and stronger guys because it regularly dispels my confidence that I have truly absorbed the fundamental beginner-intermediate aiki subset. Elements work but I find losing control easier because there's no cheating here. You can't use a little force here and there to supplement the 'correct' way of doing things. Not without getting a forceful of resistance you can't possibly overpower.

For example doing sankyo last night against my uke who's taller and stronger, once you get him down keeping him there is messy if don't maintain control on his centre. You can't take control with your strength because he is stronger. You may make use of torque and leverage, that will give you the advantage, but in the end the use of such strength really shows that we're doing it the wrong way. And once he has achieved a certain height and position, you lose whatever leverage anyway and then you start thinking ok lets cranking his hands and resorting to pain and positioning. Come the day you meet someone who can take the pain, you lose again. And so you then say ok lets do henka waza... the fact that we've gone here is basically just to pick up the pieces i.e. survival mode.

Personally I won't want to try to bring uke up once I got him there. Especially if we don't want to use any of our strength. The element I desperately need to master is to ensure I can cancel his upwards resistance that comes from a stronger arm, leg and back muscles and height. Bouncing is less effective because I'm having trouble balancing the upwards amplitude against my force, and giving him space to move in for a strike. Load bearing? Power dampening? Might be an answer, in fact it did have a measure of success.

Actually it was the least tiring way of accomplishing my goal last night. Channeling his upwards force into my structure and into the ground and reversing it to bring him down. But then where is the 'sankyo' element of controlling? Where does the image of us holding uke up with sankyo come from?

Draw strength from stillness. Learn to act without acting. And never underestimate a samurai cat.

I feel like I need a Physics degree to understand what's going on in here... But I like it. In a way I can catch glimpses of how we can describe what has been largely an indescribable element of Aikido.

See the shapes; "get" the shapes; look for the shapes. If you get nothing more, it was worth the trouble, because you will see them over and over again if you look.

Quote:

Ahmad Abas wrote:

What I would have generally described as the non-mechanical aspect of Aikido i.e. the Aiki or Mind-Energy-Body unity part is now hereto being described aptly as being mechanical/physics still. Does this help in the learning of it? Apparently so if Erick's students are to be believed.

To be clear. I use traditional terms to express the action in traditional training of aiki taiso and working through waza (always in variants, never by rote). I don't do white board lecture on a mat. We practice Aikido -- not physics. Saotome's legacy is safe because it is mainly through his students did that I learned to see it this way -- though there isn't one of them that would speak of it the way I have come to -- they showed me what I have seen -- with some good input from Saito's approach along the way.

I use what I have come to understand in this way mainly to critically correct bad action -- and to be able to explain WHY I am making the correction and why the action was bad. I cannot emphasize too much how that helps a student --- that there is not only a demonstrable HOW, but an independently intelligible WHY in each instance, and if asked I can tell them precisely why. It helps them to see the error as they do it more readily and then self-correct.

The WHY is the part that was not readily available without more mechanical concepts of action. There are components of neuromuscular action going on -- but those follow from the nature of the mechanics, because those systems they are sensitive to and use those mechanics. I would analogize the tradition as the meat of the blade -- what I am doing is analogous to polishing -- in the technical sense -- deeply involved in precise geometries and shapes consistent with the nature of the action of the weapon -- which is immensely critical to blade performance -- NOT the shiny rub on granny's silver. And there are other forms of polishing that are also effective.

Quote:

Ahmad Abas wrote:

Does it require actual/extensive physical instruction or can it be done just by understanding the concept as introduced by Erick to learn though... I wonder.

Nothing substitutes for extensive physical instruction and lots of self-critical effort. Nothing. Anybody who says different is selling something.

Quote:

Ahmad Abas wrote:

Grounding incoming force and projecting the 'earth' into various parts of the body, extending it beyond our body into uke, taking uke's center, leading not forcing, wave/bouncing, impulse/ateru... I've seen it, felt it, heard it described from the esoteric to the scientific way, and it boils down to how well we can duplicate what we feel. If we can't make our body do what we are thinking of doing,

You had me till the last -- I truly think that unless our body acts without thinking we are not yet doing proper aikido -- certainly not takemusu. And thinking about feeling is a step remove ed from feeling and acting. My approach puts the thinking apart from the subjective feeling, letting the feeling remain unmediated by thought, and directs thought toward the objective form and action, which is more amenable to thinking in the first place. IMO.

Quote:

Ahmad Abas wrote:

For example doing sankyo last night against my uke who's taller and stronger, once you get him down keeping him there is messy if don't maintain control on his centre. You can't take control with your strength because he is stronger. You may make use of torque and leverage,

Leverage won't work - or in any event is not aiki -- but the strong guys WILL use leverage -- it's what makes the "strong" after all. But in every lever there is a inherent shear -- if you use the shear -- he can't do a thing about it -- more lever = more shear. Figuring out where the shear is going (hint: right angles, always) and that's where seeing the shapes matter immensely -- and then you can correlate the shape to the feeling in the action.

Quote:

Ahmad Abas wrote:

Actually it was the least tiring way of accomplishing my goal last night. Channeling his upwards force into my structure and into the ground and reversing it to bring him down. But then where is the 'sankyo' element of controlling? Where does the image of us holding uke up with sankyo come from?

Uke has three pillars when down in a sankyo -- two legs and a bracing arm. Take a dinner plate. Put it on three pillars. Put your spread fingertips on the plate. Twist your hand with slight pressure on the surface of the plate. See what happens. That is torsional shear -- and there is your sankyo control. The more he works to get up the more vulnerable to it he becomes.

"You had me till the last -- I truly think that unless our body acts without thinking we are not yet doing proper aikido -- certainly not takemusu."

I agree... not takemusu aiki... I know I get the 'Don't think, do' a lot. Must be all that Star Wars reruns I keep watching messing with me. But at beginner-intermediate, I still have to run my intent through my head. I don't particularly concentrate on body part now though... I just feel whole body movement in relation to uke instead. I'll definitely post something here when I achieve takemusu aiki for real... when that century comes.

Googling shear stress and looking at the images, I'm confronted by a page that has equations in it that reminded me why I have up physics before college. Funnily enough, it also had an image of our arteries because of the curvature that results in shear stress in our blood flow. Anyway, it was fun trying to kick start my brain again, maybe that's why most teachers just fall back to Feel don't Think mode. :P

Draw strength from stillness. Learn to act without acting. And never underestimate a samurai cat.

I can't add anything to a scientific analysis. However, someone might find the following useful, in regards to thinking of the body as a collection of tubes, particularly the torso (hips on up).

This isn't exactly what I'm practicing from a visualization standpoint, but it's the best I can come up with from a "feel" perspective (at least for now). If your torso is a collection of tubes, try imagining incoming or outgoing forces/stresses as a pinball. The tubes can be curved or straight, as long as there are no right angles or kinks. Take the lower-back as an example. If I push open a door, the incoming force may cause my lower back to tighten, creating a kink or corner that the pinball will hit, causing it to ricochet chaotically, on it's way to finding the ground -- if it ever gets there. If instead, I keep a relaxed "hanging" tension all the way around my waist, the ball can ride a nice curve, or plonk straight down through the tube, directly to the ground. If I keep too much tension all the way around my waist or in one spot, the tube will be so constricted that the pinball will simply stop, as it can't get through.

This can still work BTW, if you're using the straight "ground-path" technique from contact point, to middle, to ground. If the ground path is directing the force, then the pinball can represent any undo tension, that is allowed to fall to the ground along with the incoming force.

I can't add anything to a scientific analysis. However, someone might find the following useful, in regards to thinking of the body as a collection of tubes, particularly the torso (hips on up).

This isn't exactly what I'm practicing from a visualization standpoint, but it's the best I can come up with from a "feel" perspective (at least for now). If your torso is a collection of tubes, try imagining incoming or outgoing forces/stresses as a pinball. The tubes can be curved or straight, as long as there are no right angles or kinks. If I keep too much tension all the way around my waist or in one spot, the tube will be so constricted that the pinball will simply stop, as it can't get through.

The concept you are articulating is more commonly called the "funicular curve" (the shape assumed by a cable or chain with arbitrary loads suspended from it) -- which also works inverted as an arch-ish form. Gaudi designed cathedrals this way. The shape supporting only its own weight is a catenary.

This is Coulomb's self-supporting catenary arch of tangent spheres illustrating the very point you have suggested, in slightly different imagery, and intensely more precarious and critical geometry.